Function Composition/Decomposition
Let f(x)= 2x and g(x)= -x - 4
Find f(g(x))
-2x - 8
What is the inverse notation?
F-1(x)
Solve using elimination
2y + 7x = -5
5y - 7x = 12
X= -1
Y= 1
When solving for an augmented matrix, can you multiply the elements of any row by 0?
No; the elements must be multiplied by a non-zero number.
How do you determine the domain of a graph?
By looking at the X-axis
Let g(x)= 3x + 2 and f(x) = 2x2 + 5
Find g(f(2))
41
Find the inverse of F(x)= 2x-1
F-1(x)= x-1/2
Solve using elimination
11x + 4y =-46
7x - 4y = 10
Y= -6
What is the main characteristic of row echelon form?
All elements below the main diagonal are zero
Can a function have two outputs for one input?
No
H= f(g)
H(x)= (x+5)2
g(x)= x+5
f(x)= x2
Find the inverse of G(x)= x-5/4
G-1(x)= 4x+5
Solve using elimination
8y−9x=−3
5y−8x=10
X= -5
Y= -6
What is the main characteristic of reduced row echelon form?
All elements above or below the main diagonal are zero
What is one easy way to tell if a graph is a function or not?
The vertical line test
G(f(x))= 2/x2+4
G(x)= 2/x
F(x)= x2+4
What is the first step when finding the inverse of a function?
Switch X and Y
Solve using elimination
10y−11x=−4
−2y+3x=4
X= 4
Y= 4
x+y+z= 6
2x+ 3y−z= 3
x+y+ 2z= 10
X= -1
Y= 3
Z= 4
What is my favorite vegetable?
Carrots
F(g(x))= (2x-1)5
F(x)= x5
G(x)= 2x-1
How can you confirm that your inverse function is correct (graphically)?
It reflects over the Y=X line
Solve using substitution
−4x+3y=−2
y=x−1
X= -1
Y= -2
5x - 4y = -10
-x + y = 2
X= -2
Y= 0
When is your exam?
September 9!